Details

analyze1.1s (15.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
25%	74.9%	0.1%	6
25%	74.9%	0.1%	7
25%	74.9%	0.1%	8
25%	74.9%	0.1%	9
25%	64%	11.1%	10
31.2%	54.6%	14.2%	11
39%	44.1%	16.9%	12
39%	41.5%	19.5%	13
42.9%	37%	20.1%	14

Compiler

Compiled 23 to 16 computations (30.4% saved)

sample4.1s (58.2%)

Results

1.1s	1898×	body	1024	valid
973.0ms	1624×	body	1024	invalid
848.0ms	4996×	body	128	valid
401.0ms	888×	body	512	valid
358.0ms	781×	body	512	invalid
150.0ms	470×	body	256	valid
122.0ms	373×	body	256	invalid
113.0ms	679×	body	128	invalid
3.0ms	4×	body	2048	valid

preprocess27.0ms (0.4%)

Algorithm

2×	egg-herbie

Rules

96×	`fma-def_binary64`
70×	`*-commutative_binary64`
57×	`associate-/l*_binary64`
30×	`associate-/r/_binary64`
26×	`distribute-rgt-out_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	80
1	69	72
2	160	72
3	243	72
4	321	72
5	375	72
6	420	72
7	474	72
8	480	72
0	3	3
1	3	3

Stop Event

1×	unsound
1×	saturated

Calls

Call 1

Inputs
0
1
2

Outputs
0
1
0
2

Call 2

Inputs
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)))
(+.f64 (.f64 (/.f64 (cos.f64 a1) (sqrt.f64 2)) (.f64 th th)) (.f64 (/.f64 (cos.f64 a1) (sqrt.f64 2)) (.f64 a2 a2)))
(+.f64 (.f64 (/.f64 (cos.f64 a2) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 a2) (sqrt.f64 2)) (.f64 th th)))

Outputs
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a1 a1 (.f64 a2 a2)))
(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a1 a1 (.f64 a2 a2)))
(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
(+.f64 (.f64 (/.f64 (cos.f64 a1) (sqrt.f64 2)) (.f64 th th)) (.f64 (/.f64 (cos.f64 a1) (sqrt.f64 2)) (.f64 a2 a2)))
(.f64 (/.f64 (cos.f64 a1) (sqrt.f64 2)) (+.f64 (.f64 th th) (*.f64 a2 a2)))
(.f64 (/.f64 (cos.f64 a1) (sqrt.f64 2)) (fma.f64 th th (.f64 a2 a2)))
(.f64 (cos.f64 a1) (/.f64 (fma.f64 th th (.f64 a2 a2)) (sqrt.f64 2)))
(+.f64 (.f64 (/.f64 (cos.f64 a2) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 a2) (sqrt.f64 2)) (.f64 th th)))
(.f64 (/.f64 (cos.f64 a2) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 th th)))
(.f64 (/.f64 (cos.f64 a2) (sqrt.f64 2)) (fma.f64 a1 a1 (.f64 th th)))
(.f64 (/.f64 (cos.f64 a2) (sqrt.f64 2)) (fma.f64 th th (.f64 a1 a1)))

Symmetry

(sort a1 a2)

Compiler

Compiled 22 to 15 computations (31.8% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

32×	`fma-def_binary64`
23×	`*-commutative_binary64`
20×	`associate-/l*_binary64`
11×	`associate-/r/_binary64`
9×	`associate-*r/_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	20
1	27	18
2	58	18
3	88	18
4	115	18
5	135	18
6	152	18
7	170	18
8	172	18

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

Inputs
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))

Outputs
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a1 a1 (.f64 a2 a2)))
(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))

prune5.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.3b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.4b	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
	0.4b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))

Compiler

Compiled 108 to 70 computations (35.2% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a1 a1 (*.f64 a2 a2))
✓	0.1b	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
✓	0.4b	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))

series17.0ms (0.2%)

Counts

3 → 84

Calls

21 calls:

Time	Variable		Point	Expression
3.0ms	a2	@	inf	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
2.0ms	th	@	inf	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
1.0ms	a1	@	0	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))
1.0ms	a1	@	0	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
1.0ms	th	@	0	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))

rewrite49.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

523×	`log-prod_binary64`
195×	`expm1-udef_binary64`
195×	`log1p-udef_binary64`
182×	`pow3_binary64`
171×	`log-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	39
1	224	36
2	2729	36

Stop Event

1×	node limit

Counts

3 → 94

Calls

Call 1

Inputs
(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))
(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
(fma.f64 a1 a1 (*.f64 a2 a2))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)))) (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))) (cbrt.f64 (/.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 2) 2)) (cbrt.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) 2) (.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (pow.f64 2 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (hypot.f64 a1 a2) (pow.f64 2 1/4)) (/.f64 (hypot.f64 a1 a2) (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (hypot.f64 a1 a2) (.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (neg.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (/.f64 1 (neg.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 2 -1/2) (pow.f64 (hypot.f64 a1 a2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) 2) 1) (/.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (hypot.f64 a1 a2) 1) (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (cbrt.f64 2)) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cbrt.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) 2) (cbrt.f64 2)) (cbrt.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (hypot.f64 a1 a2) (cbrt.f64 2)) (/.f64 (hypot.f64 a1 a2) (cbrt.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (pow.f64 2 1/4)) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) 2) (pow.f64 2 1/4)) (/.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (hypot.f64 a1 a2) (pow.f64 2 1/4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (neg.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 3) (.f64 2 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (pow.f64 (exp.f64 (cos.f64 th)) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)))) (cbrt.f64 (pow.f64 (exp.f64 (cos.f64 th)) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (cos.f64 th)) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (cos.f64 th)) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (cos.f64 th)) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (sqrt.f64 2) (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th)) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th))) (neg.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th)) 1) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th)) (cbrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th)) (pow.f64 2 1/4)) (pow.f64 2 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (neg.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (cos.f64 th)) (neg.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (cos.f64 th) (neg.f64 (pow.f64 (hypot.f64 a1 a2) 2))) (neg.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (/.f64 (hypot.f64 a1 a2) (pow.f64 2 1/4)) (sqrt.f64 (cos.f64 th))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 2) (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (cos.f64 th)) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) 3) (pow.f64 (cos.f64 th) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (cos.f64 th) 3) (pow.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 a2 a2) (.f64 a1 a1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 a1 a1) (.f64 a2 a2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (hypot.f64 a1 a2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (.f64 a1 a1) 1) (.f64 a2 a2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (pow.f64 (hypot.f64 a1 a2) 2))) (cbrt.f64 (exp.f64 (pow.f64 (hypot.f64 a1 a2) 2))))) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (hypot.f64 a1 a2) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (hypot.f64 a1 a2) 2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (hypot.f64 a1 a2) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (hypot.f64 a1 a2) 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (hypot.f64 a1 a2) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (pow.f64 (hypot.f64 a1 a2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) 2) (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (hypot.f64 a1 a2) (hypot.f64 a1 a2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (.f64 a1 a1) 3) (pow.f64 (.f64 a2 a2) 3)) (fma.f64 (.f64 a1 a1) (.f64 a1 a1) (-.f64 (pow.f64 a2 4) (.f64 (.f64 a1 a1) (.f64 a2 a2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 (.f64 a1 a1) (.f64 a1 a1)) (pow.f64 a2 4)) (-.f64 (.f64 a1 a1) (.f64 a2 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 a1 a2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (hypot.f64 a1 a2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (hypot.f64 a1 a2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (pow.f64 (exp.f64 a2) a2) (exp.f64 (.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (+.f64 1 (expm1.f64 (.f64 a2 a2))) (exp.f64 (.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (exp.f64 (.f64 a1 a1)) (+.f64 1 (expm1.f64 (.f64 a2 a2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (hypot.f64 a1 a2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (hypot.f64 a1 a2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 2 (log.f64 (hypot.f64 a1 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 2 (log.f64 (hypot.f64 a1 a2))) 1))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)))) (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))) (cbrt.f64 (/.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 2) 2)) (cbrt.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) 2) (*.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (pow.f64 2 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (hypot.f64 a1 a2) (pow.f64 2 1/4)) (/.f64 (hypot.f64 a1 a2) (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 a1 a2) (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (/.f64 1 (neg.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 2 -1/2) (pow.f64 (hypot.f64 a1 a2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) 2) 1) (/.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (hypot.f64 a1 a2) 1) (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 2)) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cbrt.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) 2) (cbrt.f64 2)) (cbrt.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (hypot.f64 a1 a2) (cbrt.f64 2)) (/.f64 (hypot.f64 a1 a2) (cbrt.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 2 1/4)) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) 2) (pow.f64 2 1/4)) (/.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (hypot.f64 a1 a2) (pow.f64 2 1/4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (neg.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 3) (*.f64 2 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))) 1))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (pow.f64 (exp.f64 (cos.f64 th)) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)))) (cbrt.f64 (pow.f64 (exp.f64 (cos.f64 th)) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (cos.f64 th)) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (cos.f64 th)) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (cos.f64 th)) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (sqrt.f64 2) (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th)) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th))) (neg.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th)) 1) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th)) (cbrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th)) (pow.f64 2 1/4)) (pow.f64 2 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (neg.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (cos.f64 th)) (neg.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (cos.f64 th) (neg.f64 (pow.f64 (hypot.f64 a1 a2) 2))) (neg.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 (hypot.f64 a1 a2) (pow.f64 2 1/4)) (sqrt.f64 (cos.f64 th))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 2) (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (cos.f64 th)) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) 3) (pow.f64 (cos.f64 th) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (cos.f64 th) 3) (pow.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))) 1))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 a2 a2) (*.f64 a1 a1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 a1 a1) (*.f64 a2 a2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (hypot.f64 a1 a2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 a1 a1) 1) (*.f64 a2 a2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (pow.f64 (hypot.f64 a1 a2) 2))) (cbrt.f64 (exp.f64 (pow.f64 (hypot.f64 a1 a2) 2))))) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (hypot.f64 a1 a2) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (hypot.f64 a1 a2) 2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (hypot.f64 a1 a2) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (hypot.f64 a1 a2) 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (hypot.f64 a1 a2) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (hypot.f64 a1 a2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) 2) (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 a1 a2) (hypot.f64 a1 a2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 a1 a1) 3) (pow.f64 (*.f64 a2 a2) 3)) (fma.f64 (*.f64 a1 a1) (*.f64 a1 a1) (-.f64 (pow.f64 a2 4) (*.f64 (*.f64 a1 a1) (*.f64 a2 a2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 a1 a1) (*.f64 a1 a1)) (pow.f64 a2 4)) (-.f64 (*.f64 a1 a1) (*.f64 a2 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 a1 a2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (hypot.f64 a1 a2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (hypot.f64 a1 a2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (pow.f64 (exp.f64 a2) a2) (exp.f64 (*.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (*.f64 a2 a2))) (exp.f64 (*.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (*.f64 a1 a1)) (+.f64 1 (expm1.f64 (*.f64 a2 a2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (hypot.f64 a1 a2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (hypot.f64 a1 a2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 2 (log.f64 (hypot.f64 a1 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 2 (log.f64 (hypot.f64 a1 a2))) 1))))))

simplify51.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

821×	`unswap-sqr_binary64`
650×	`associate-l_binary64`
423×	`fma-def_binary64`
199×	`associate-/l*_binary64`
171×	`*-commutative_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	47	1447
1	107	1343
2	286	1339
3	1023	1271
4	3816	1271

Stop Event

1×	node limit

Counts

178 → 122

Calls

Call 1

Inputs
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(/.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2)))))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2))) (.f64 1/24 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)) (sqrt.f64 2))))))
(+.f64 (.f64 -1/720 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 6)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2))) (.f64 1/24 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)) (sqrt.f64 2)))))))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(pow.f64 a2 2)
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(pow.f64 a1 2)
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(pow.f64 a1 2)
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(pow.f64 a1 2)
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(pow.f64 a2 2)
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(pow.f64 a2 2)
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))

Outputs
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(fma.f64 (/.f64 a1 (sqrt.f64 2)) a1 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(fma.f64 (/.f64 a1 (sqrt.f64 2)) a1 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(fma.f64 (/.f64 a1 (sqrt.f64 2)) a1 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(fma.f64 (/.f64 a1 (sqrt.f64 2)) a1 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(fma.f64 (/.f64 a1 (sqrt.f64 2)) a1 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(fma.f64 (/.f64 a1 (sqrt.f64 2)) a1 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(fma.f64 (/.f64 a1 (sqrt.f64 2)) a1 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(fma.f64 (/.f64 a1 (sqrt.f64 2)) a1 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(fma.f64 (/.f64 a1 (sqrt.f64 2)) a1 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(fma.f64 (/.f64 a1 (sqrt.f64 2)) a1 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(fma.f64 (/.f64 a1 (sqrt.f64 2)) a1 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(fma.f64 (/.f64 a1 (sqrt.f64 2)) a1 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(fma.f64 (/.f64 a1 (sqrt.f64 2)) a1 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(fma.f64 (/.f64 a1 (sqrt.f64 2)) a1 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(fma.f64 (/.f64 a1 (sqrt.f64 2)) a1 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(fma.f64 (/.f64 a1 (sqrt.f64 2)) a1 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(fma.f64 (/.f64 a1 (sqrt.f64 2)) a1 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(fma.f64 (/.f64 a1 (sqrt.f64 2)) a1 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(/.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (sqrt.f64 2))
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (sqrt.f64 2))
(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2)))))
(+.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2))) (.f64 -1/2 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (.f64 th th)))))
(+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (fma.f64 -1/2 (/.f64 (.f64 th th) (/.f64 (sqrt.f64 2) (fma.f64 a1 a1 (.f64 a2 a2)))) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))))
(fma.f64 -1/2 (.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)) (.f64 th th)) (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2))))
(fma.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)) (.f64 -1/2 (*.f64 th th)) (fma.f64 (/.f64 a1 (sqrt.f64 2)) a1 (/.f64 a2 (/.f64 (sqrt.f64 2) a2))))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2))) (.f64 1/24 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)) (sqrt.f64 2))))))
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(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (fma.f64 a1 a1 (*.f64 a2 a2))))
(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)) (cos.f64 th))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (fma.f64 a1 a1 (*.f64 a2 a2))))
(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)) (cos.f64 th))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (fma.f64 a1 a1 (*.f64 a2 a2))))
(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)) (cos.f64 th))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(pow.f64 a2 2)
(*.f64 a2 a2)
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(fma.f64 a1 a1 (*.f64 a2 a2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(fma.f64 a1 a1 (*.f64 a2 a2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(fma.f64 a1 a1 (*.f64 a2 a2))
(pow.f64 a1 2)
(*.f64 a1 a1)
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(fma.f64 a1 a1 (*.f64 a2 a2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(fma.f64 a1 a1 (*.f64 a2 a2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(fma.f64 a1 a1 (*.f64 a2 a2))
(pow.f64 a1 2)
(*.f64 a1 a1)
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(fma.f64 a1 a1 (*.f64 a2 a2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(fma.f64 a1 a1 (*.f64 a2 a2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(fma.f64 a1 a1 (*.f64 a2 a2))
(pow.f64 a1 2)
(*.f64 a1 a1)
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(fma.f64 a1 a1 (*.f64 a2 a2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(fma.f64 a1 a1 (*.f64 a2 a2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(fma.f64 a1 a1 (*.f64 a2 a2))
(pow.f64 a2 2)
(*.f64 a2 a2)
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(fma.f64 a1 a1 (*.f64 a2 a2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(fma.f64 a1 a1 (*.f64 a2 a2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(fma.f64 a1 a1 (*.f64 a2 a2))
(pow.f64 a2 2)
(*.f64 a2 a2)
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(fma.f64 a1 a1 (*.f64 a2 a2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(fma.f64 a1 a1 (*.f64 a2 a2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(fma.f64 a1 a1 (*.f64 a2 a2))

prune205.0ms (2.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	114	8	122
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	116	8	124

Error

Counts

124 → 8

Alt Table

Status	Error	Program
	0.5b	(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))))
	0.4b	(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
	0.4b	(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
	0.5b	(/.f64 (/.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th)) (pow.f64 2 1/4)) (pow.f64 2 1/4))
	0.5b	(.f64 (cos.f64 th) (.f64 (pow.f64 2 -1/2) (pow.f64 (hypot.f64 a1 a2) 2)))
	0.7b	(.f64 (cos.f64 th) (.f64 (/.f64 1 (pow.f64 2 1/4)) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 1/4))))
	1.9b	(pow.f64 (cbrt.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))) 3)
▶	0.4b	(*.f64 (cos.f64 th) (fma.f64 (/.f64 a1 (sqrt.f64 2)) a1 (/.f64 a2 (/.f64 (sqrt.f64 2) a2))))

Compiler

Compiled 2298 to 1477 computations (35.7% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (cos.f64 th) (fma.f64 (/.f64 a1 (sqrt.f64 2)) a1 (/.f64 a2 (/.f64 (sqrt.f64 2) a2))))
✓	0.2b	(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
✓	0.4b	(/.f64 (sqrt.f64 2) a2)
✓	0.4b	(/.f64 a1 (sqrt.f64 2))

series16.0ms (0.2%)

Counts

4 → 48

Calls

18 calls:

Time	Variable		Point	Expression
6.0ms	a2	@	0	(*.f64 (cos.f64 th) (fma.f64 (/.f64 a1 (sqrt.f64 2)) a1 (/.f64 a2 (/.f64 (sqrt.f64 2) a2))))
1.0ms	th	@	inf	(*.f64 (cos.f64 th) (fma.f64 (/.f64 a1 (sqrt.f64 2)) a1 (/.f64 a2 (/.f64 (sqrt.f64 2) a2))))
1.0ms	th	@	0	(*.f64 (cos.f64 th) (fma.f64 (/.f64 a1 (sqrt.f64 2)) a1 (/.f64 a2 (/.f64 (sqrt.f64 2) a2))))
1.0ms	a1	@	0	(*.f64 (cos.f64 th) (fma.f64 (/.f64 a1 (sqrt.f64 2)) a1 (/.f64 a2 (/.f64 (sqrt.f64 2) a2))))
1.0ms	a1	@	inf	(/.f64 a1 (sqrt.f64 2))

rewrite57.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

367×	`prod-diff_binary64`
229×	`expm1-udef_binary64`
229×	`log1p-udef_binary64`
129×	`add-sqr-sqrt_binary64`
126×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	44
1	255	44
2	3370	44

Stop Event

1×	node limit

Counts

4 → 126

Calls

Call 1

Inputs
(/.f64 a1 (sqrt.f64 2))
(/.f64 (sqrt.f64 2) a2)
(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
(*.f64 (cos.f64 th) (fma.f64 (/.f64 a1 (sqrt.f64 2)) a1 (/.f64 a2 (/.f64 (sqrt.f64 2) a2))))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 a1 (sqrt.f64 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 a1 (pow.f64 2 -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 a1 (sqrt.f64 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (/.f64 a1 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 a1 (sqrt.f64 2))) (cbrt.f64 (/.f64 (.f64 a1 a1) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 (.f64 a1 a1) 2)) (cbrt.f64 (/.f64 a1 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 a1) 2) (.f64 (cbrt.f64 a1) (pow.f64 2 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (/.f64 a1 (sqrt.f64 2))) (sqrt.f64 (/.f64 a1 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 a1) (.f64 (sqrt.f64 a1) (pow.f64 2 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (neg.f64 a1) (/.f64 1 (neg.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 2 -1/2) a1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 a1) 2) 1) (/.f64 (cbrt.f64 a1) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 a1) 1) (/.f64 (sqrt.f64 a1) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (cbrt.f64 2)) (/.f64 a1 (cbrt.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 a1) 2) (cbrt.f64 2)) (cbrt.f64 (/.f64 a1 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 a1) (cbrt.f64 2)) (/.f64 (sqrt.f64 a1) (cbrt.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (pow.f64 2 1/4)) (/.f64 a1 (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 a1) 2) (pow.f64 2 1/4)) (/.f64 (cbrt.f64 a1) (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 a1 (sqrt.f64 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 a1 (sqrt.f64 2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 a1 (sqrt.f64 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 a1 (sqrt.f64 2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 2) a1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 a1 (neg.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (.f64 a1 a1) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 a1 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 a1 (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 a1 (sqrt.f64 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 a1 3) (.f64 2 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 a1 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 a1 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 a1 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (/.f64 a1 (sqrt.f64 2))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (sqrt.f64 2) a2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 2) (/.f64 1 a2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 2) a2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (/.f64 (sqrt.f64 2) a2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 2) (.f64 (cbrt.f64 (sqrt.f64 2)) (/.f64 1 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 (sqrt.f64 2) a2)) (cbrt.f64 (/.f64 2 (.f64 a2 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 2 (.f64 a2 a2))) (cbrt.f64 (/.f64 (sqrt.f64 2) a2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (/.f64 (sqrt.f64 2) a2)) (sqrt.f64 (/.f64 (sqrt.f64 2) a2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) (/.f64 1 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (neg.f64 (sqrt.f64 2)) (/.f64 1 (neg.f64 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 a2) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (cbrt.f64 2) 1) (/.f64 (cbrt.f64 (sqrt.f64 2)) a2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 2 1/4) 1) (/.f64 (pow.f64 2 1/4) a2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (pow.f64 (cbrt.f64 a2) 2)) (/.f64 (sqrt.f64 2) (cbrt.f64 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (sqrt.f64 a2)) (/.f64 (sqrt.f64 2) (sqrt.f64 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (cbrt.f64 2) (pow.f64 (cbrt.f64 a2) 2)) (cbrt.f64 (/.f64 (sqrt.f64 2) a2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 2 1/4) (pow.f64 (cbrt.f64 a2) 2)) (/.f64 (pow.f64 2 1/4) (cbrt.f64 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (cbrt.f64 2) (sqrt.f64 a2)) (/.f64 (cbrt.f64 (sqrt.f64 2)) (sqrt.f64 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 2) a2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (sqrt.f64 2) a2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) a2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) a2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 a2 (sqrt.f64 2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (sqrt.f64 2) (neg.f64 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 2 (.f64 a2 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (sqrt.f64 2) a2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (sqrt.f64 2) a2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 2) a2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (.f64 2 (sqrt.f64 2)) (pow.f64 a2 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (sqrt.f64 2) a2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (sqrt.f64 2) a2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (sqrt.f64 2) a2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (/.f64 (sqrt.f64 2) a2)) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 a2 (/.f64 a2 (sqrt.f64 2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 a2 (/.f64 a2 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 a2 (/.f64 a2 (sqrt.f64 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (.f64 a2 (/.f64 a2 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (.f64 a2 (/.f64 a2 (sqrt.f64 2)))) (pow.f64 (cbrt.f64 (.f64 a2 (/.f64 a2 (sqrt.f64 2)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (.f64 a2 (/.f64 a2 (sqrt.f64 2)))) 2) (cbrt.f64 (.f64 a2 (/.f64 a2 (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 a2) 2) (.f64 (cbrt.f64 a2) (/.f64 a2 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (.f64 a2 (/.f64 a2 (sqrt.f64 2)))) (sqrt.f64 (.f64 a2 (/.f64 a2 (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 a2) (.f64 (sqrt.f64 a2) (/.f64 a2 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (neg.f64 a2) (/.f64 1 (/.f64 (neg.f64 (sqrt.f64 2)) a2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 a2 (sqrt.f64 2)) a2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 2 -1/2) (/.f64 a2 (/.f64 1 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 a2) 2) (sqrt.f64 2)) (/.f64 (cbrt.f64 a2) (/.f64 1 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 a2) (sqrt.f64 2)) (/.f64 (sqrt.f64 a2) (/.f64 1 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 a2) 2) 1) (/.f64 (cbrt.f64 a2) (/.f64 (sqrt.f64 2) a2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 a2) 1) (/.f64 (sqrt.f64 a2) (/.f64 (sqrt.f64 2) a2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (cbrt.f64 (/.f64 2 (.f64 a2 a2)))) (/.f64 a2 (cbrt.f64 (/.f64 (sqrt.f64 2) a2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 a2) 2) (cbrt.f64 (/.f64 2 (.f64 a2 a2)))) (cbrt.f64 (.f64 a2 (/.f64 a2 (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 a2) (cbrt.f64 (/.f64 2 (.f64 a2 a2)))) (/.f64 (sqrt.f64 a2) (cbrt.f64 (/.f64 (sqrt.f64 2) a2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (sqrt.f64 (/.f64 (sqrt.f64 2) a2))) (/.f64 a2 (sqrt.f64 (/.f64 (sqrt.f64 2) a2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 a2) 2) (sqrt.f64 (/.f64 (sqrt.f64 2) a2))) (/.f64 (cbrt.f64 a2) (sqrt.f64 (/.f64 (sqrt.f64 2) a2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 a2 1) (/.f64 a2 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 a2 (neg.f64 (sqrt.f64 2))) (neg.f64 a2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (/.f64 a2 (sqrt.f64 2)) 1) a2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (/.f64 a2 (sqrt.f64 2)) (pow.f64 (cbrt.f64 a2) 2)) (cbrt.f64 a2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (/.f64 a2 (sqrt.f64 2)) (sqrt.f64 a2)) (sqrt.f64 a2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 a2 (/.f64 a2 (sqrt.f64 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 a2 (/.f64 a2 (sqrt.f64 2))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 a2 (/.f64 a2 (sqrt.f64 2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 a2 (/.f64 a2 (sqrt.f64 2)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 2) (.f64 a2 a2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 a2 (/.f64 (neg.f64 (sqrt.f64 2)) a2)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (.f64 a2 (/.f64 a2 (sqrt.f64 2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 a2) (/.f64 a2 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 a2 (/.f64 a2 (sqrt.f64 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 a2 (/.f64 a2 (sqrt.f64 2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 a2 3) (pow.f64 (/.f64 (sqrt.f64 2) a2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 a2 (/.f64 a2 (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 a2 (/.f64 a2 (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 a2 (/.f64 a2 (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 a2 (/.f64 a2 (sqrt.f64 2)))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2)) (cos.f64 th)) (.f64 (.f64 a2 (/.f64 a2 (sqrt.f64 2))) (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2))) (.f64 (cos.f64 th) (.f64 a2 (/.f64 a2 (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 (cos.f64 th) (fma.f64 a2 (/.f64 a2 (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (cos.f64 th) (fma.f64 a2 (/.f64 a2 (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 (cos.f64 th) (fma.f64 a2 (/.f64 a2 (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 (cos.f64 th) (fma.f64 a2 (/.f64 a2 (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 (cos.f64 th) (fma.f64 a2 (/.f64 a2 (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (.f64 (cos.f64 th) (fma.f64 a2 (/.f64 a2 (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (cos.f64 th)) (fma.f64 a2 (/.f64 a2 (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 (cos.f64 th) (fma.f64 a2 (/.f64 a2 (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 (cos.f64 th) (fma.f64 a2 (/.f64 a2 (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (cos.f64 th) 3) (pow.f64 (fma.f64 a2 (/.f64 a2 (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (fma.f64 a2 (/.f64 a2 (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2))) 3) (pow.f64 (cos.f64 th) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)) (.f64 (cos.f64 th) (.f64 a2 (/.f64 a2 (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2)) (cos.f64 th) (.f64 (.f64 a2 (/.f64 a2 (sqrt.f64 2))) (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 (cos.f64 th) (fma.f64 a2 (/.f64 a2 (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 (cos.f64 th) (fma.f64 a2 (/.f64 a2 (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 (cos.f64 th) (fma.f64 a2 (/.f64 a2 (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 (cos.f64 th) (fma.f64 a2 (/.f64 a2 (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2))))) 1))))))

simplify34.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

749×	`associate-l_binary64`
700×	`fma-def_binary64`
592×	`associate-r_binary64`
193×	`associate-+l+_binary64`
147×	`associate-+r+_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	39	1100
1	91	1096
2	282	1026
3	1106	857

Stop Event

1×	node limit

Counts

174 → 143

Calls

Call 1

Inputs
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (.f64 -1/2 (.f64 (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2))) (pow.f64 th 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2))))
(+.f64 (.f64 -1/2 (.f64 (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2))) (pow.f64 th 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (.f64 1/24 (.f64 (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2))) (pow.f64 th 4))))))
(+.f64 (.f64 -1/720 (.f64 (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2))) (pow.f64 th 6))) (+.f64 (.f64 -1/2 (.f64 (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2))) (pow.f64 th 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (.f64 1/24 (.f64 (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2))) (pow.f64 th 4)))))))
(*.f64 (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2))) (cos.f64 th))
(*.f64 (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2))) (cos.f64 th))
(*.f64 (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2))) (cos.f64 th))
(*.f64 (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2))) (cos.f64 th))
(*.f64 (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2))) (cos.f64 th))
(*.f64 (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2))) (cos.f64 th))
(*.f64 (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2))) (cos.f64 th))
(*.f64 (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2))) (cos.f64 th))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))

Outputs
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(fma.f64 (/.f64 a1 (sqrt.f64 2)) a1 (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))
(+.f64 (.f64 -1/2 (.f64 (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2))) (pow.f64 th 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2))))
(fma.f64 -1/2 (.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2))) (.f64 th th)) (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2))))
(fma.f64 -1/2 (.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))) (.f64 th th)) (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))))
(.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))))
(.f64 (fma.f64 (/.f64 a1 (sqrt.f64 2)) a1 (/.f64 (.f64 a2 a2) (sqrt.f64 2))) (fma.f64 -1/2 (*.f64 th th) 1))
(+.f64 (.f64 -1/2 (.f64 (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2))) (pow.f64 th 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (.f64 1/24 (.f64 (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2))) (pow.f64 th 4))))))
(fma.f64 -1/2 (.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2))) (.f64 th th)) (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (+.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2)) (.f64 1/24 (.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2))) (pow.f64 th 4))))))
(+.f64 (fma.f64 1/24 (.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))) (pow.f64 th 4)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))) (fma.f64 -1/2 (.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))) (.f64 th th)) (/.f64 (.f64 a2 a2) (sqrt.f64 2))))
(+.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) a1)) (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))) (+.f64 (.f64 1/24 (pow.f64 th 4)) (.f64 -1/2 (.f64 th th))))))
(.f64 (fma.f64 (/.f64 a1 (sqrt.f64 2)) a1 (/.f64 (.f64 a2 a2) (sqrt.f64 2))) (+.f64 (.f64 1/24 (pow.f64 th 4)) (fma.f64 -1/2 (.f64 th th) 1)))
(+.f64 (.f64 -1/720 (.f64 (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2))) (pow.f64 th 6))) (+.f64 (.f64 -1/2 (.f64 (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2))) (pow.f64 th 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (.f64 1/24 (.f64 (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2))) (pow.f64 th 4)))))))
(fma.f64 -1/720 (.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2))) (pow.f64 th 6)) (fma.f64 -1/2 (.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2))) (.f64 th th)) (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (+.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2)) (.f64 1/24 (.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2))) (pow.f64 th 4)))))))
(fma.f64 -1/720 (.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))) (pow.f64 th 6)) (+.f64 (fma.f64 1/24 (.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))) (pow.f64 th 4)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))) (fma.f64 -1/2 (.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))) (.f64 th th)) (/.f64 (.f64 a2 a2) (sqrt.f64 2)))))
(+.f64 (.f64 (+.f64 (.f64 1/24 (pow.f64 th 4)) 1) (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))) (.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))) (+.f64 (.f64 -1/2 (.f64 th th)) (.f64 -1/720 (pow.f64 th 6)))))
(fma.f64 (fma.f64 (/.f64 a1 (sqrt.f64 2)) a1 (/.f64 (.f64 a2 a2) (sqrt.f64 2))) (fma.f64 -1/720 (pow.f64 th 6) (.f64 -1/2 (.f64 th th))) (.f64 (fma.f64 (/.f64 a1 (sqrt.f64 2)) a1 (/.f64 (*.f64 a2 a2) (sqrt.f64 2))) (fma.f64 1/24 (pow.f64 th 4) 1)))
(*.f64 (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2))) (cos.f64 th))
(.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2))) (cos.f64 th))
(.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))) (cos.f64 th))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(*.f64 (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2))) (cos.f64 th))
(.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2))) (cos.f64 th))
(.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))) (cos.f64 th))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(*.f64 (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2))) (cos.f64 th))
(.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2))) (cos.f64 th))
(.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))) (cos.f64 th))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(*.f64 (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2))) (cos.f64 th))
(.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2))) (cos.f64 th))
(.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))) (cos.f64 th))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(*.f64 (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2))) (cos.f64 th))
(.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2))) (cos.f64 th))
(.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))) (cos.f64 th))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(*.f64 (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2))) (cos.f64 th))
(.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2))) (cos.f64 th))
(.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))) (cos.f64 th))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(*.f64 (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2))) (cos.f64 th))
(.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2))) (cos.f64 th))
(.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))) (cos.f64 th))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(*.f64 (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2))) (cos.f64 th))
(.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2))) (cos.f64 th))
(.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))) (cos.f64 th))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (cos.f64 th))
(.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2))) (cos.f64 th))
(.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))) (cos.f64 th))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2))) (cos.f64 th))
(.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))) (cos.f64 th))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2))) (cos.f64 th))
(.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))) (cos.f64 th))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(*.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) a1)) (cos.f64 th))
(.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2))) (cos.f64 th))
(.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))) (cos.f64 th))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2))) (cos.f64 th))
(.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))) (cos.f64 th))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2))) (cos.f64 th))
(.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))) (cos.f64 th))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(*.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) a1)) (cos.f64 th))
(.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2))) (cos.f64 th))
(.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))) (cos.f64 th))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2))) (cos.f64 th))
(.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))) (cos.f64 th))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2))) (cos.f64 th))
(.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))) (cos.f64 th))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(*.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) a1)) (cos.f64 th))
(.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2))) (cos.f64 th))
(.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))) (cos.f64 th))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2))) (cos.f64 th))
(.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))) (cos.f64 th))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2))) (cos.f64 th))
(.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))) (cos.f64 th))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (cos.f64 th))
(.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2))) (cos.f64 th))
(.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))) (cos.f64 th))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2))) (cos.f64 th))
(.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))) (cos.f64 th))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2))) (cos.f64 th))
(.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))) (cos.f64 th))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (cos.f64 th))
(.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2))) (cos.f64 th))
(.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))) (cos.f64 th))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2))) (cos.f64 th))
(.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))) (cos.f64 th))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2))) (cos.f64 th))
(.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))) (cos.f64 th))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))

prune314.0ms (4.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	139	4	143
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	144	7	151

Error

Counts

151 → 7

Alt Table

Status	Error	Program
▶	0.4b	(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
	0.4b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
	0.5b	(/.f64 (/.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th)) (pow.f64 2 1/4)) (pow.f64 2 1/4))
	0.4b	(*.f64 (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2))) (cos.f64 th))
	0.4b	(.f64 (cos.f64 th) (fma.f64 (/.f64 a1 (sqrt.f64 2)) a1 (/.f64 a2 (.f64 (/.f64 (pow.f64 2 1/4) 1) (/.f64 (pow.f64 2 1/4) a2)))))
	0.5b	(.f64 (cos.f64 th) (.f64 (pow.f64 2 -1/2) (pow.f64 (hypot.f64 a1 a2) 2)))
	0.8b	(*.f64 (cos.f64 th) (fma.f64 (pow.f64 (cbrt.f64 (/.f64 a1 (sqrt.f64 2))) 3) a1 (/.f64 a2 (/.f64 (sqrt.f64 2) a2))))

Compiler

Compiled 3096 to 2053 computations (33.7% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
✓	0.1b	(*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th))
✓	0.3b	(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))

series11.0ms (0.2%)

Counts

3 → 62

Calls

24 calls:

Time	Variable		Point	Expression
1.0ms	a1	@	0	(*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th))
1.0ms	a2	@	0	(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
1.0ms	a2	@	inf	(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
1.0ms	a2	@	-inf	(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
1.0ms	th	@	inf	(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))

rewrite54.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

634×	`prod-diff_binary64`
220×	`log1p-udef_binary64`
130×	`add-sqr-sqrt_binary64`
128×	`pow1_binary64`
126×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	45
1	261	36
2	3419	36

Stop Event

1×	node limit

Counts

3 → 101

Calls

Call 1

Inputs
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)) (cos.f64 th)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 1 (/.f64 (sqrt.f64 2) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (hypot.f64 a2 a1) 2) (*.f64 (cos.f64 th) (pow.f64 2 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cos.f64 th) (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (pow.f64 2 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th)) (pow.f64 2 -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)) (cos.f64 th)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)) (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)) (cos.f64 th))) (cbrt.f64 (/.f64 (pow.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th)) 2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th)) 2) 2)) (cbrt.f64 (*.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th))) 2) (*.f64 (cbrt.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th))) (pow.f64 2 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (cos.f64 th)) (hypot.f64 a2 a1)) (*.f64 (*.f64 (sqrt.f64 (cos.f64 th)) (hypot.f64 a2 a1)) (pow.f64 2 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cos.f64 th) (neg.f64 (pow.f64 (hypot.f64 a2 a1) 2))) (/.f64 1 (neg.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 2 -1/2) (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) 1) (/.f64 (cos.f64 th) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cos.f64 th) 1) (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)) (cos.f64 th))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th))) 2) 1) (/.f64 (cbrt.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th))) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 (sqrt.f64 (cos.f64 th)) (hypot.f64 a2 a1)) 1) (/.f64 (*.f64 (sqrt.f64 (cos.f64 th)) (hypot.f64 a2 a1)) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cbrt.f64 2)) (/.f64 (cos.f64 th) (cbrt.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cos.f64 th) (cbrt.f64 2)) (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cbrt.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 2)) (/.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th)) (cbrt.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th))) 2) (cbrt.f64 2)) (cbrt.f64 (*.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 (sqrt.f64 (cos.f64 th)) (hypot.f64 a2 a1)) (cbrt.f64 2)) (/.f64 (*.f64 (sqrt.f64 (cos.f64 th)) (hypot.f64 a2 a1)) (cbrt.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (pow.f64 2 1/4)) (/.f64 (cos.f64 th) (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cos.f64 th) (pow.f64 2 1/4)) (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 2 1/4)) (/.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th)) (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th))) 2) (pow.f64 2 1/4)) (/.f64 (cbrt.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th))) (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)) (cos.f64 th)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)) (cos.f64 th)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)) (cos.f64 th))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a2 a1) 2)) (cos.f64 th)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th)) (neg.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (pow.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th)) 2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (*.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)) (cos.f64 th)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)) (cos.f64 th)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th)) 3) (*.f64 2 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)) (cos.f64 th))) 1))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 a2 a2) (cos.f64 th)) (*.f64 (*.f64 a1 a1) (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 a1 a1) (cos.f64 th)) (*.f64 (*.f64 a2 a2) (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (cos.f64 th) (*.f64 a2 a2)) (*.f64 (cos.f64 th) (*.f64 a1 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (cos.f64 th) (*.f64 a1 a1)) (*.f64 (cos.f64 th) (*.f64 a2 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6)) (cos.f64 th)) (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a2 a1) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (cos.f64 th)) (-.f64 (*.f64 a2 a2) (*.f64 a1 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (cos.f64 th) (+.f64 (pow.f64 a2 6) (pow.f64 a1 6))) (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a2 a1) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (cos.f64 th) (-.f64 (pow.f64 a2 4) (pow.f64 a1 4))) (-.f64 (*.f64 a2 a2) (*.f64 a1 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 (cos.f64 th)) (hypot.f64 a2 a1)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (pow.f64 (hypot.f64 a2 a1) 2)) (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (pow.f64 (hypot.f64 a2 a1) 2) 3) (pow.f64 (cos.f64 th) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (cos.f64 th) 3) (pow.f64 (pow.f64 (hypot.f64 a2 a1) 2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th))) 1))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (hypot.f64 a2 a1) 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 a2 4) (-.f64 (*.f64 a2 a2) (*.f64 a1 a1))) (/.f64 (pow.f64 a1 4) (-.f64 (*.f64 a2 a2) (*.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (hypot.f64 a2 a1) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (hypot.f64 a2 a1) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) 2) (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 a2 a1) (hypot.f64 a2 a1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6)) (/.f64 1 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a2 a1) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (/.f64 1 (-.f64 (*.f64 a2 a2) (*.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a2 a1) 2))) (+.f64 (pow.f64 a2 6) (pow.f64 a1 6))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (-.f64 (pow.f64 a2 4) (pow.f64 a1 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6)) (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a2 a1) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6)) (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (*.f64 a2 a1) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (-.f64 (*.f64 a2 a2) (*.f64 a1 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6))) (neg.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a2 a1) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4))) (neg.f64 (-.f64 (*.f64 a2 a2) (*.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (-.f64 (*.f64 a1 a1) (*.f64 a2 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (hypot.f64 a2 a1) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 (hypot.f64 a2 a1) 2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 a2 a1) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (pow.f64 (hypot.f64 a2 a1) 2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (hypot.f64 a2 a1) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (hypot.f64 a2 a1) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 a2 a1) 2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 a2 a2 (*.f64 a1 a1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 a1 a1 (*.f64 a2 a2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 a2 a2) (*.f64 a1 a1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 a1 a1) (*.f64 a2 a2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 a1 4)) (pow.f64 (cbrt.f64 a1) 2) (*.f64 a2 a2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 a2 4)) (cbrt.f64 (*.f64 a2 a2)) (*.f64 a1 a1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (hypot.f64 a2 a1) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (hypot.f64 a2 a1) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (pow.f64 (hypot.f64 a2 a1) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (hypot.f64 a2 a1) 2)) 1))))))

simplify50.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

690×	`associate-+r+_binary64`
505×	`unswap-sqr_binary64`
262×	`associate-/l*_binary64`
247×	`*-commutative_binary64`
237×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	57	1411
1	141	1279
2	436	1161
3	1630	1003
4	4573	1003

Stop Event

1×	node limit

Counts

163 → 133

Calls

Call 1

Inputs
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2)))))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2))) (.f64 1/24 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)) (sqrt.f64 2))))))
(+.f64 (.f64 -1/720 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 6)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2))) (.f64 1/24 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)) (sqrt.f64 2)))))))
(*.f64 (pow.f64 a1 2) (cos.f64 th))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(*.f64 (pow.f64 a1 2) (cos.f64 th))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(*.f64 (pow.f64 a1 2) (cos.f64 th))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a2 2) (+.f64 (pow.f64 a1 2) (.f64 -1/2 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)))))
(+.f64 (pow.f64 a2 2) (+.f64 (pow.f64 a1 2) (+.f64 (.f64 -1/2 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2))) (.f64 1/24 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4))))))
(+.f64 (pow.f64 a2 2) (+.f64 (pow.f64 a1 2) (+.f64 (.f64 -1/2 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2))) (+.f64 (.f64 1/24 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4))) (.f64 -1/720 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 6)))))))
(pow.f64 a1 2)
(pow.f64 a2 2)
(pow.f64 a2 2)
(pow.f64 a2 2)
(pow.f64 a1 2)
(pow.f64 a1 2)

Outputs
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (.f64 (.f64 a1 a1) (cos.f64 th)) (sqrt.f64 2))
(*.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) a1)) (cos.f64 th))
(*.f64 (cos.f64 th) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(.f64 (cos.f64 th) (.f64 a1 (/.f64 a1 (sqrt.f64 2))))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (.f64 a1 a1) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (*.f64 a2 a2))))
(+.f64 (.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) a1)) (cos.f64 th)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)))
(.f64 (cos.f64 th) (+.f64 (.f64 (/.f64 a2 (sqrt.f64 2)) a2) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))))
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(+.f64 (.f64 a2 (/.f64 a2 (sqrt.f64 2))) (+.f64 (fma.f64 -1/2 (.f64 th (/.f64 (.f64 th (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 2))) (.f64 a1 (/.f64 a1 (sqrt.f64 2)))) (.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)) (+.f64 (.f64 -1/720 (pow.f64 th 6)) (*.f64 1/24 (pow.f64 th 4))))))
(*.f64 (pow.f64 a1 2) (cos.f64 th))
(.f64 (.f64 a1 a1) (cos.f64 th))
(.f64 a1 (.f64 a1 (cos.f64 th)))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(fma.f64 (cos.f64 th) (.f64 a2 a2) (.f64 (*.f64 a1 a1) (cos.f64 th)))
(.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))
(.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1)))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(fma.f64 (cos.f64 th) (.f64 a2 a2) (.f64 (*.f64 a1 a1) (cos.f64 th)))
(.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))
(.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1)))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(fma.f64 (cos.f64 th) (.f64 a2 a2) (.f64 (*.f64 a1 a1) (cos.f64 th)))
(.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))
(.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1)))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(.f64 (cos.f64 th) (.f64 a2 a2))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(fma.f64 (cos.f64 th) (.f64 a2 a2) (.f64 (*.f64 a1 a1) (cos.f64 th)))
(.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))
(.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1)))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(fma.f64 (cos.f64 th) (.f64 a2 a2) (.f64 (*.f64 a1 a1) (cos.f64 th)))
(.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))
(.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1)))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(fma.f64 (cos.f64 th) (.f64 a2 a2) (.f64 (*.f64 a1 a1) (cos.f64 th)))
(.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))
(.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1)))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(.f64 (cos.f64 th) (.f64 a2 a2))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(fma.f64 (cos.f64 th) (.f64 a2 a2) (.f64 (*.f64 a1 a1) (cos.f64 th)))
(.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))
(.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1)))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(fma.f64 (cos.f64 th) (.f64 a2 a2) (.f64 (*.f64 a1 a1) (cos.f64 th)))
(.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))
(.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1)))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(fma.f64 (cos.f64 th) (.f64 a2 a2) (.f64 (*.f64 a1 a1) (cos.f64 th)))
(.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))
(.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1)))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(.f64 (cos.f64 th) (.f64 a2 a2))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(fma.f64 (cos.f64 th) (.f64 a2 a2) (.f64 (*.f64 a1 a1) (cos.f64 th)))
(.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))
(.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1)))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(fma.f64 (cos.f64 th) (.f64 a2 a2) (.f64 (*.f64 a1 a1) (cos.f64 th)))
(.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))
(.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1)))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(fma.f64 (cos.f64 th) (.f64 a2 a2) (.f64 (*.f64 a1 a1) (cos.f64 th)))
(.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))
(.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1)))
(*.f64 (pow.f64 a1 2) (cos.f64 th))
(.f64 (.f64 a1 a1) (cos.f64 th))
(.f64 a1 (.f64 a1 (cos.f64 th)))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(fma.f64 (cos.f64 th) (.f64 a2 a2) (.f64 (*.f64 a1 a1) (cos.f64 th)))
(.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))
(.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1)))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(fma.f64 (cos.f64 th) (.f64 a2 a2) (.f64 (*.f64 a1 a1) (cos.f64 th)))
(.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))
(.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1)))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(fma.f64 (cos.f64 th) (.f64 a2 a2) (.f64 (*.f64 a1 a1) (cos.f64 th)))
(.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))
(.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1)))
(*.f64 (pow.f64 a1 2) (cos.f64 th))
(.f64 (.f64 a1 a1) (cos.f64 th))
(.f64 a1 (.f64 a1 (cos.f64 th)))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(fma.f64 (cos.f64 th) (.f64 a2 a2) (.f64 (*.f64 a1 a1) (cos.f64 th)))
(.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))
(.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1)))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(fma.f64 (cos.f64 th) (.f64 a2 a2) (.f64 (*.f64 a1 a1) (cos.f64 th)))
(.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))
(.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1)))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(fma.f64 (cos.f64 th) (.f64 a2 a2) (.f64 (*.f64 a1 a1) (cos.f64 th)))
(.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))
(.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1)))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (.f64 a1 a1) (.f64 a2 a2))
(fma.f64 a1 a1 (*.f64 a2 a2))
(fma.f64 a2 a2 (*.f64 a1 a1))
(+.f64 (pow.f64 a2 2) (+.f64 (pow.f64 a1 2) (.f64 -1/2 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)))))
(+.f64 (.f64 a2 a2) (+.f64 (.f64 a1 a1) (.f64 -1/2 (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (*.f64 th th)))))
(fma.f64 a2 a2 (fma.f64 a1 a1 (.f64 (.f64 -1/2 (.f64 th th)) (fma.f64 a1 a1 (.f64 a2 a2)))))
(.f64 (+.f64 (.f64 th (.f64 th -1/2)) 1) (fma.f64 a2 a2 (.f64 a1 a1)))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (+.f64 1 (.f64 -1/2 (.f64 th th))))
(+.f64 (pow.f64 a2 2) (+.f64 (pow.f64 a1 2) (+.f64 (.f64 -1/2 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2))) (.f64 1/24 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4))))))
(+.f64 (.f64 a2 a2) (+.f64 (.f64 a1 a1) (fma.f64 -1/2 (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (.f64 th th)) (.f64 1/24 (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (pow.f64 th 4))))))
(fma.f64 a2 a2 (fma.f64 a1 a1 (fma.f64 -1/2 (.f64 th (.f64 th (fma.f64 a1 a1 (.f64 a2 a2)))) (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (pow.f64 th 4) 1/24)))))
(fma.f64 a1 a1 (fma.f64 a2 a2 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (+.f64 (.f64 th (.f64 th -1/2)) (*.f64 1/24 (pow.f64 th 4))))))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (+.f64 (.f64 -1/2 (.f64 th th)) (+.f64 1 (*.f64 1/24 (pow.f64 th 4)))))
(+.f64 (pow.f64 a2 2) (+.f64 (pow.f64 a1 2) (+.f64 (.f64 -1/2 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2))) (+.f64 (.f64 1/24 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4))) (.f64 -1/720 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 6)))))))
(+.f64 (.f64 a2 a2) (+.f64 (.f64 a1 a1) (fma.f64 -1/2 (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (.f64 th th)) (fma.f64 1/24 (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (pow.f64 th 4)) (.f64 (.f64 -1/720 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) (pow.f64 th 6))))))
(fma.f64 a2 a2 (fma.f64 a1 a1 (fma.f64 -1/2 (.f64 th (.f64 th (fma.f64 a1 a1 (.f64 a2 a2)))) (fma.f64 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) 1/24) (pow.f64 th 4) (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (pow.f64 th 6) -1/720))))))
(+.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (+.f64 (.f64 th (.f64 th -1/2)) (.f64 -1/720 (pow.f64 th 6)))) (.f64 (+.f64 (.f64 1/24 (pow.f64 th 4)) 1) (fma.f64 a2 a2 (.f64 a1 a1))))
(fma.f64 a1 a1 (fma.f64 a2 a2 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (+.f64 (.f64 1/24 (pow.f64 th 4)) (+.f64 (.f64 -1/720 (pow.f64 th 6)) (.f64 -1/2 (.f64 th th)))))))
(pow.f64 a1 2)
(*.f64 a1 a1)
(pow.f64 a2 2)
(*.f64 a2 a2)
(pow.f64 a2 2)
(*.f64 a2 a2)
(pow.f64 a2 2)
(*.f64 a2 a2)
(pow.f64 a1 2)
(*.f64 a1 a1)
(pow.f64 a1 2)
(*.f64 a1 a1)

prune222.0ms (3.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	132	1	133
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	133	7	140

Error

Counts

140 → 7

Alt Table

Status	Error	Program
✓	0.4b	(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
	0.4b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
	0.5b	(/.f64 (/.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th)) (pow.f64 2 1/4)) (pow.f64 2 1/4))
	0.5b	(.f64 (cos.f64 th) (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (pow.f64 2 -1/2)))
▶	0.4b	(*.f64 (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2))) (cos.f64 th))
	0.4b	(.f64 (cos.f64 th) (fma.f64 (/.f64 a1 (sqrt.f64 2)) a1 (/.f64 a2 (.f64 (/.f64 (pow.f64 2 1/4) 1) (/.f64 (pow.f64 2 1/4) a2)))))
	0.8b	(*.f64 (cos.f64 th) (fma.f64 (pow.f64 (cbrt.f64 (/.f64 a1 (sqrt.f64 2))) 3) a1 (/.f64 a2 (/.f64 (sqrt.f64 2) a2))))

Compiler

Compiled 2598 to 1637 computations (37% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
✓	0.1b	(*.f64 (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2))) (cos.f64 th))
✓	0.3b	(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
✓	0.3b	(/.f64 (pow.f64 a2 2) (sqrt.f64 2))

series18.0ms (0.3%)

Counts

4 → 34

Calls

21 calls:

Time	Variable		Point	Expression
10.0ms	a2	@	inf	(*.f64 (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2))) (cos.f64 th))
1.0ms	th	@	inf	(*.f64 (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2))) (cos.f64 th))
1.0ms	a2	@	0	(*.f64 (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2))) (cos.f64 th))
1.0ms	a1	@	inf	(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
1.0ms	th	@	-inf	(*.f64 (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2))) (cos.f64 th))

rewrite79.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

432×	`fma-def_binary64`
246×	`expm1-udef_binary64`
246×	`log1p-udef_binary64`
231×	`fma-neg_binary64`
144×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	13	63
1	287	55
2	3942	51

Stop Event

1×	node limit

Counts

4 → 178

Calls

Call 1

Inputs
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(*.f64 (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2))) (cos.f64 th))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 a2 (.f64 a2 (pow.f64 2 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 a2 a2) (pow.f64 2 -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (/.f64 (.f64 a2 a2) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2))) (cbrt.f64 (/.f64 (pow.f64 a2 4) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 (pow.f64 a2 4) 2)) (cbrt.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 a2 4)) (.f64 (pow.f64 (cbrt.f64 a2) 2) (pow.f64 2 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 a2 (pow.f64 2 1/4)) (/.f64 a2 (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 a2 (neg.f64 a2)) (/.f64 1 (neg.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 2 -1/2) (.f64 a2 a2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (cbrt.f64 2)) (/.f64 (.f64 a2 a2) (cbrt.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (pow.f64 2 1/4)) (/.f64 (.f64 a2 a2) (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 a2 1) (/.f64 a2 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (cbrt.f64 (pow.f64 a2 4)) 1) (/.f64 (pow.f64 (cbrt.f64 a2) 2) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 a2 (cbrt.f64 2)) (/.f64 a2 (cbrt.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (cbrt.f64 (pow.f64 a2 4)) (cbrt.f64 2)) (cbrt.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (cbrt.f64 (pow.f64 a2 4)) (pow.f64 2 1/4)) (/.f64 (pow.f64 (cbrt.f64 a2) 2) (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 a2 (pow.f64 2 1/4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 2) (.f64 a2 a2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (.f64 a2 a2) (neg.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (pow.f64 a2 4) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 2))) 1))))))
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simplify37.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

749×	`associate-l_binary64`
700×	`fma-def_binary64`
583×	`associate-r_binary64`
197×	`associate-+l+_binary64`
149×	`associate-+r+_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	38	936
1	89	932
2	274	772
3	1096	643

Stop Event

1×	node limit

Counts

212 → 196

Calls

Call 1

Inputs
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (.f64 -1/2 (.f64 (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2))) (pow.f64 th 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2))))
(+.f64 (.f64 -1/2 (.f64 (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2))) (pow.f64 th 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (.f64 1/24 (.f64 (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2))) (pow.f64 th 4))))))
(+.f64 (.f64 -1/720 (.f64 (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2))) (pow.f64 th 6))) (+.f64 (.f64 -1/2 (.f64 (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2))) (pow.f64 th 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (.f64 1/24 (.f64 (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2))) (pow.f64 th 4)))))))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))

Outputs
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
(.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th))) (/.f64 (.f64 (cos.f64 th) (*.f64 a2 a2)) (sqrt.f64 2)))
(+.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (.f64 a1 a1))) (.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 2)) (cos.f64 th)))
(.f64 (cos.f64 th) (+.f64 (.f64 (/.f64 a2 (sqrt.f64 2)) a2) (*.f64 (/.f64 a1 (sqrt.f64 2)) a1)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th))) (/.f64 (.f64 (cos.f64 th) (*.f64 a2 a2)) (sqrt.f64 2)))
(+.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (.f64 a1 a1))) (.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 2)) (cos.f64 th)))
(.f64 (cos.f64 th) (+.f64 (.f64 (/.f64 a2 (sqrt.f64 2)) a2) (*.f64 (/.f64 a1 (sqrt.f64 2)) a1)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th))) (/.f64 (.f64 (cos.f64 th) (*.f64 a2 a2)) (sqrt.f64 2)))
(+.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (.f64 a1 a1))) (.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 2)) (cos.f64 th)))
(.f64 (cos.f64 th) (+.f64 (.f64 (/.f64 a2 (sqrt.f64 2)) a2) (*.f64 (/.f64 a1 (sqrt.f64 2)) a1)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2))
(.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (cos.f64 th))
(.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(.f64 a2 (.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th))) (/.f64 (.f64 (cos.f64 th) (*.f64 a2 a2)) (sqrt.f64 2)))
(+.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (.f64 a1 a1))) (.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 2)) (cos.f64 th)))
(.f64 (cos.f64 th) (+.f64 (.f64 (/.f64 a2 (sqrt.f64 2)) a2) (*.f64 (/.f64 a1 (sqrt.f64 2)) a1)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th))) (/.f64 (.f64 (cos.f64 th) (*.f64 a2 a2)) (sqrt.f64 2)))
(+.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (.f64 a1 a1))) (.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 2)) (cos.f64 th)))
(.f64 (cos.f64 th) (+.f64 (.f64 (/.f64 a2 (sqrt.f64 2)) a2) (*.f64 (/.f64 a1 (sqrt.f64 2)) a1)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th))) (/.f64 (.f64 (cos.f64 th) (*.f64 a2 a2)) (sqrt.f64 2)))
(+.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (.f64 a1 a1))) (.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 2)) (cos.f64 th)))
(.f64 (cos.f64 th) (+.f64 (.f64 (/.f64 a2 (sqrt.f64 2)) a2) (*.f64 (/.f64 a1 (sqrt.f64 2)) a1)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2))
(.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (cos.f64 th))
(.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(.f64 a2 (.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th))) (/.f64 (.f64 (cos.f64 th) (*.f64 a2 a2)) (sqrt.f64 2)))
(+.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (.f64 a1 a1))) (.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 2)) (cos.f64 th)))
(.f64 (cos.f64 th) (+.f64 (.f64 (/.f64 a2 (sqrt.f64 2)) a2) (*.f64 (/.f64 a1 (sqrt.f64 2)) a1)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th))) (/.f64 (.f64 (cos.f64 th) (*.f64 a2 a2)) (sqrt.f64 2)))
(+.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (.f64 a1 a1))) (.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 2)) (cos.f64 th)))
(.f64 (cos.f64 th) (+.f64 (.f64 (/.f64 a2 (sqrt.f64 2)) a2) (*.f64 (/.f64 a1 (sqrt.f64 2)) a1)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th))) (/.f64 (.f64 (cos.f64 th) (*.f64 a2 a2)) (sqrt.f64 2)))
(+.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (.f64 a1 a1))) (.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 2)) (cos.f64 th)))
(.f64 (cos.f64 th) (+.f64 (.f64 (/.f64 a2 (sqrt.f64 2)) a2) (*.f64 (/.f64 a1 (sqrt.f64 2)) a1)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2))
(.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (cos.f64 th))
(.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(.f64 a2 (.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th))) (/.f64 (.f64 (cos.f64 th) (*.f64 a2 a2)) (sqrt.f64 2)))
(+.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (.f64 a1 a1))) (.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 2)) (cos.f64 th)))
(.f64 (cos.f64 th) (+.f64 (.f64 (/.f64 a2 (sqrt.f64 2)) a2) (*.f64 (/.f64 a1 (sqrt.f64 2)) a1)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th))) (/.f64 (.f64 (cos.f64 th) (*.f64 a2 a2)) (sqrt.f64 2)))
(+.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (.f64 a1 a1))) (.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 2)) (cos.f64 th)))
(.f64 (cos.f64 th) (+.f64 (.f64 (/.f64 a2 (sqrt.f64 2)) a2) (*.f64 (/.f64 a1 (sqrt.f64 2)) a1)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th))) (/.f64 (.f64 (cos.f64 th) (*.f64 a2 a2)) (sqrt.f64 2)))
(+.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (.f64 a1 a1))) (.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 2)) (cos.f64 th)))
(.f64 (cos.f64 th) (+.f64 (.f64 (/.f64 a2 (sqrt.f64 2)) a2) (*.f64 (/.f64 a1 (sqrt.f64 2)) a1)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
(.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th))) (/.f64 (.f64 (cos.f64 th) (*.f64 a2 a2)) (sqrt.f64 2)))
(+.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (.f64 a1 a1))) (.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 2)) (cos.f64 th)))
(.f64 (cos.f64 th) (+.f64 (.f64 (/.f64 a2 (sqrt.f64 2)) a2) (*.f64 (/.f64 a1 (sqrt.f64 2)) a1)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th))) (/.f64 (.f64 (cos.f64 th) (*.f64 a2 a2)) (sqrt.f64 2)))
(+.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (.f64 a1 a1))) (.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 2)) (cos.f64 th)))
(.f64 (cos.f64 th) (+.f64 (.f64 (/.f64 a2 (sqrt.f64 2)) a2) (*.f64 (/.f64 a1 (sqrt.f64 2)) a1)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th))) (/.f64 (.f64 (cos.f64 th) (*.f64 a2 a2)) (sqrt.f64 2)))
(+.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (.f64 a1 a1))) (.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 2)) (cos.f64 th)))
(.f64 (cos.f64 th) (+.f64 (.f64 (/.f64 a2 (sqrt.f64 2)) a2) (*.f64 (/.f64 a1 (sqrt.f64 2)) a1)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
(.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th))) (/.f64 (.f64 (cos.f64 th) (*.f64 a2 a2)) (sqrt.f64 2)))
(+.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (.f64 a1 a1))) (.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 2)) (cos.f64 th)))
(.f64 (cos.f64 th) (+.f64 (.f64 (/.f64 a2 (sqrt.f64 2)) a2) (*.f64 (/.f64 a1 (sqrt.f64 2)) a1)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th))) (/.f64 (.f64 (cos.f64 th) (*.f64 a2 a2)) (sqrt.f64 2)))
(+.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (.f64 a1 a1))) (.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 2)) (cos.f64 th)))
(.f64 (cos.f64 th) (+.f64 (.f64 (/.f64 a2 (sqrt.f64 2)) a2) (*.f64 (/.f64 a1 (sqrt.f64 2)) a1)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th))) (/.f64 (.f64 (cos.f64 th) (*.f64 a2 a2)) (sqrt.f64 2)))
(+.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (.f64 a1 a1))) (.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 2)) (cos.f64 th)))
(.f64 (cos.f64 th) (+.f64 (.f64 (/.f64 a2 (sqrt.f64 2)) a2) (*.f64 (/.f64 a1 (sqrt.f64 2)) a1)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(+.f64 (.f64 (/.f64 a2 (sqrt.f64 2)) a2) (.f64 (/.f64 a1 (sqrt.f64 2)) a1))
(fma.f64 (/.f64 a2 (sqrt.f64 2)) a2 (/.f64 (*.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (.f64 -1/2 (.f64 (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2))) (pow.f64 th 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2))))
(fma.f64 -1/2 (.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2))) (.f64 th th)) (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2))))
(+.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) a1)) (fma.f64 -1/2 (.f64 th (.f64 th (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))))) (/.f64 (.f64 a2 a2) (sqrt.f64 2))))
(.f64 (+.f64 (.f64 th (.f64 th -1/2)) 1) (+.f64 (.f64 (/.f64 a2 (sqrt.f64 2)) a2) (*.f64 (/.f64 a1 (sqrt.f64 2)) a1)))
(.f64 (fma.f64 (/.f64 a2 (sqrt.f64 2)) a2 (/.f64 (.f64 a1 a1) (sqrt.f64 2))) (fma.f64 th (*.f64 th -1/2) 1))
(+.f64 (.f64 -1/2 (.f64 (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2))) (pow.f64 th 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (.f64 1/24 (.f64 (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2))) (pow.f64 th 4))))))
(fma.f64 -1/2 (.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2))) (.f64 th th)) (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (+.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2)) (.f64 1/24 (.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2))) (pow.f64 th 4))))))
(+.f64 (fma.f64 1/24 (.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))) (pow.f64 th 4)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))) (fma.f64 -1/2 (.f64 th (.f64 th (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))))) (/.f64 (.f64 a2 a2) (sqrt.f64 2))))
(+.f64 (+.f64 (.f64 (/.f64 a2 (sqrt.f64 2)) a2) (.f64 (/.f64 a1 (sqrt.f64 2)) a1)) (.f64 (+.f64 (.f64 (/.f64 a2 (sqrt.f64 2)) a2) (.f64 (/.f64 a1 (sqrt.f64 2)) a1)) (+.f64 (.f64 1/24 (pow.f64 th 4)) (.f64 th (.f64 th -1/2)))))
(.f64 (fma.f64 (/.f64 a2 (sqrt.f64 2)) a2 (/.f64 (.f64 a1 a1) (sqrt.f64 2))) (+.f64 (.f64 1/24 (pow.f64 th 4)) (fma.f64 th (.f64 th -1/2) 1)))
(+.f64 (.f64 -1/720 (.f64 (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2))) (pow.f64 th 6))) (+.f64 (.f64 -1/2 (.f64 (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2))) (pow.f64 th 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (.f64 1/24 (.f64 (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2))) (pow.f64 th 4)))))))
(fma.f64 -1/720 (.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2))) (pow.f64 th 6)) (fma.f64 -1/2 (.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2))) (.f64 th th)) (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (+.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2)) (.f64 1/24 (.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2))) (pow.f64 th 4)))))))
(fma.f64 -1/720 (.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))) (pow.f64 th 6)) (+.f64 (fma.f64 1/24 (.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))) (pow.f64 th 4)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))) (fma.f64 -1/2 (.f64 th (.f64 th (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))))) (/.f64 (.f64 a2 a2) (sqrt.f64 2)))))
(+.f64 (.f64 (+.f64 (.f64 1/24 (pow.f64 th 4)) 1) (+.f64 (.f64 (/.f64 a2 (sqrt.f64 2)) a2) (.f64 (/.f64 a1 (sqrt.f64 2)) a1))) (.f64 (+.f64 (.f64 (/.f64 a2 (sqrt.f64 2)) a2) (.f64 (/.f64 a1 (sqrt.f64 2)) a1)) (+.f64 (.f64 th (.f64 th -1/2)) (.f64 -1/720 (pow.f64 th 6)))))
(fma.f64 (fma.f64 (/.f64 a2 (sqrt.f64 2)) a2 (/.f64 (.f64 a1 a1) (sqrt.f64 2))) (fma.f64 th (.f64 th -1/2) (.f64 -1/720 (pow.f64 th 6))) (.f64 (fma.f64 (/.f64 a2 (sqrt.f64 2)) a2 (/.f64 (*.f64 a1 a1) (sqrt.f64 2))) (fma.f64 1/24 (pow.f64 th 4) 1)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 (/.f64 a2 (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 (/.f64 a2 (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 (/.f64 a2 (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)

prune465.0ms (6.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	193	3	196
Fresh	2	3	5
Picked	1	0	1
Done	0	1	1
Total	196	7	203

Error

Counts

203 → 7

Alt Table

Status	Error	Program
	0.4b	(.f64 (+.f64 (.f64 (*.f64 a2 a2) (pow.f64 2 -1/2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2))) (cos.f64 th))
	0.4b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
	0.5b	(.f64 (fma.f64 (.f64 a1 a1) (pow.f64 2 -1/2) (/.f64 (*.f64 a2 a2) (sqrt.f64 2))) (cos.f64 th))
	0.4b	(.f64 (cos.f64 th) (fma.f64 (/.f64 a1 (sqrt.f64 2)) a1 (/.f64 a2 (.f64 (/.f64 (pow.f64 2 1/4) 1) (/.f64 (pow.f64 2 1/4) a2)))))
✓	0.4b	(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
	0.5b	(/.f64 (/.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th)) (pow.f64 2 1/4)) (pow.f64 2 1/4))
	0.8b	(*.f64 (cos.f64 th) (fma.f64 (pow.f64 (cbrt.f64 (/.f64 a1 (sqrt.f64 2))) 3) a1 (/.f64 a2 (/.f64 (sqrt.f64 2) a2))))

Compiler

Compiled 4260 to 2737 computations (35.8% saved)

regimes95.0ms (1.3%)

Accuracy

Total -1.9b remaining (-504.9%)

Threshold costs -1.9b (-504.9%)

Counts

18 → 1

Calls

Call 1

Inputs
(.f64 (+.f64 (.f64 (*.f64 a2 a2) (pow.f64 2 -1/2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2))) (cos.f64 th))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (fma.f64 (.f64 a1 a1) (pow.f64 2 -1/2) (/.f64 (*.f64 a2 a2) (sqrt.f64 2))) (cos.f64 th))
(.f64 (cos.f64 th) (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (pow.f64 2 -1/2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(*.f64 (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2))) (cos.f64 th))
(.f64 (cos.f64 th) (fma.f64 (/.f64 a1 (sqrt.f64 2)) a1 (/.f64 a2 (.f64 (/.f64 (pow.f64 2 1/4) 1) (/.f64 (pow.f64 2 1/4) a2)))))
(*.f64 (cos.f64 th) (fma.f64 (pow.f64 (cbrt.f64 (/.f64 a1 (sqrt.f64 2))) 3) a1 (/.f64 a2 (/.f64 (sqrt.f64 2) a2))))
(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (/.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th)) (pow.f64 2 1/4)) (pow.f64 2 1/4))
(.f64 (cos.f64 th) (.f64 (pow.f64 2 -1/2) (pow.f64 (hypot.f64 a1 a2) 2)))
(.f64 (cos.f64 th) (.f64 (/.f64 1 (pow.f64 2 1/4)) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 1/4))))
(pow.f64 (cbrt.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))) 3)
(*.f64 (cos.f64 th) (fma.f64 (/.f64 a1 (sqrt.f64 2)) a1 (/.f64 a2 (/.f64 (sqrt.f64 2) a2))))
(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))

Outputs
(*.f64 (cos.f64 th) (fma.f64 (/.f64 a1 (sqrt.f64 2)) a1 (/.f64 a2 (/.f64 (sqrt.f64 2) a2))))

Results

10.0ms	0.4b	`a1`
9.0ms	0.4b	`a2`
10.0ms	0.4b	`th`
8.0ms	0.4b	`(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))`
10.0ms	0.4b	`(/.f64 (cos.f64 th) (sqrt.f64 2))`
7.0ms	0.4b	`(/.f64 (cos.f64 th) (sqrt.f64 2))`
8.0ms	0.4b	`(cos.f64 th)`
6.0ms	0.4b	`(*.f64 a1 a1)`
6.0ms	0.4b	`(*.f64 a1 a1)`
5.0ms	0.4b	`(*.f64 a2 a2)`
5.0ms	0.4b	`(*.f64 a2 a2)`

Compiler

Compiled 354 to 223 computations (37% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	23
1	13	23

Stop Event

1×

saturated

Calls

Call 1

Inputs
(*.f64 (cos.f64 th) (fma.f64 (/.f64 a1 (sqrt.f64 2)) a1 (/.f64 a2 (/.f64 (sqrt.f64 2) a2))))

Outputs
(*.f64 (cos.f64 th) (fma.f64 (/.f64 a1 (sqrt.f64 2)) a1 (/.f64 a2 (/.f64 (sqrt.f64 2) a2))))

end33.0ms (0.5%)

Stop Event

1×

fuel

Compiler

Compiled 72 to 52 computations (27.8% saved)

Details

analyze1.1s (15.2%)

sample4.1s (58.2%)

preprocess27.0ms (0.4%)

simplify8.0ms (0.1%)

prune5.0ms (0.1%)

localize8.0ms (0.1%)

series17.0ms (0.2%)

rewrite49.0ms (0.7%)

simplify51.0ms (0.7%)

prune205.0ms (2.9%)

localize9.0ms (0.1%)

series16.0ms (0.2%)

rewrite57.0ms (0.8%)

simplify34.0ms (0.5%)

prune314.0ms (4.4%)

localize9.0ms (0.1%)

series11.0ms (0.2%)

rewrite54.0ms (0.8%)

simplify50.0ms (0.7%)

prune222.0ms (3.1%)

localize10.0ms (0.1%)

series18.0ms (0.3%)

rewrite79.0ms (1.1%)

simplify37.0ms (0.5%)

prune465.0ms (6.6%)

regimes95.0ms (1.3%)

simplify2.0ms (0%)

end33.0ms (0.5%)

Profiling